United sent Nani on a season-long loan to Sporting Lisbon as part of the deal that brought Marcos Rojo to Old Trafford last summer.
The winger revealed Woodward has been in touch to congratulate him on his good form and the midfielder appears open to the possibility of staying at United once his loan at Sporting expires.
"I love Manchester United," the Portuguese told the Guardian.
"The only decision I made (last summer) was to play more and be me again, because I lost a lot of things there last season due to injuries and the change of manager.
"You never know the future," Nani added.
"It depends on a lot of things
If United want me to stay then with a different mentality I think we can work well next season but there are a lot of things to discuss and see."
Nani has been in good form since his move to Portugal, scoring eight goals in 25 appearances.
He broke down in tears after scoring his latest goal last Sunday - a dipping long-range volley in the 2-0 win against Gil Vicente.
The 28-year-old, who joined United from Sporting in 2007, said he was overcome by emotion because of "personal stuff".
He also revealed Woodward messaged him to congratulate him on scoring the goal.
"I receive some texts from Ed Woodward," Nani said.
"He texted me about the goal [on Sunday] and the great season I am having here."
Source : PA
Source: PA